Determining trigonometric functions given their graphs

Lessons

• 1.
  For the following graph, write an equation (with the smallest phase shift) in the form of:
  (i) y = a sin b(x - c) + d
  (ii) y = - a sin b(x - c) + d
  (iii) y = a cos b(x - c) + d
  (iv) y = - a cos b(x - c) + d
  a)

  
  
  
  
  b)

  
  
  
  

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• 2.
  A sinusoidal curve has a minimum point at $\left( { - \frac{\pi }{3},\; - 5} \right)$ and the closest maximum point to the right is $\left( {\;\frac{\pi }{6},\;3} \right)$. Determine an equation of this curve.
  

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